Certain cases of loss of control over the motion of symmetrical systems

The bifurcations of periodic motions of nonlinear systems are studied, which can lead to a state in which the change in the sign of the control parameter ceases to affect the character of the nonsymmetric motion of the system. Results of the investigation of the concrete systems (piecewise connected and with power-type nonlinearity) are given, illustrating the mechanism of the appearance of a malfunction.